A Chebyshev Spectral Method with Null Space Approach for Boundary-Value Problems of Euler-Bernoulli Beam
We proposed a Chebyshev spectral method with a null space approach for investigating the boundary-value problem of a nonprismatic Euler-Bernoulli beam with generalized boundary or interface conditions. It is shown here that, with few vital improvements, a Chebyshev spectral collocation approach can...
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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2018-01-01
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| Series: | Shock and Vibration |
| Online Access: | http://dx.doi.org/10.1155/2018/2487697 |
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| Summary: | We proposed a Chebyshev spectral method with a null space approach for investigating the boundary-value problem of a nonprismatic Euler-Bernoulli beam with generalized boundary or interface conditions. It is shown here that, with few vital improvements, a Chebyshev spectral collocation approach can be systematically applied to modeling nonprismatic Euler-Bernoulli beams with eigenvalue embedded tip-massed boundary conditions as well as the jump conditions that appear at the stepped interfaces. This study also presents a numerical stable asymptotic modal solution for the higher-order modes of a partially clamped beam and show that the proposed approach validates the robust higher-order modal solutions. Through a sequence of four increasingly complicated examples, using the proposed approach with higher-order modes, generalized boundary conditions, and interface jump conditions of nonprismatic beams, the results are in excellent agreement with those reported in the literature using various other approaches. |
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| ISSN: | 1070-9622 1875-9203 |